I'm considering these texts. I really want to read (not translate where possible) Homer, and I'd like to be able to read the New Testament as well. I've limited myself to books that have an available answer key.

I'm currently working on Latin (off & on for years), I've done a fair amount of Lingua Latina, and am currently solidifying my grammar with Henle Latin. I really like the combination of LL's graded reading with the pensum & hints all in Latin plus Henle's limited vocabulary and gradual grammar practice.

I'm far from an expert, so take this with the proverbial grain of salt. However we seem to have the same taste in textbooks: I'm also reviewing what's left of my school latin with Henle and Lingua latina and like both very much. Of the textbooks you mention I used both that by Beetham and a Reading Course in Homeric Greek. I think a Reading Course in Homeric Greek is much better. Beetham is more like a crash course for someone who wants to get back into Greek after a few years, but even then the sloppy lay-out and the print that is microscopic in places makes it unpractical. However, if you have two goals so far apart (the New Testament and Homer) maybe you should go for something in between and learn Attic first.